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Задать вопрос экспертам

Консультация № 200373

03.03.2021, 16:56

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0 1 1

Образование

Здравствуйте! Прошу помощи в следующем вопросе:
Емкость конденсатора, входящего в контур, равна 1 мкФ, частота колебаний 1 кГц. При t=0 конденсатор имеет максимальный заряд, равный 10 мкКл.
Найти:
4) индуктивность контура;
5) в какой момент времени сила тока впервые достигнет максимума;
6) в какой момент времени заряд конденсатора впервые станет равным 5 мкКл.

Обсуждение

давно

Посетитель
226425
1567

06.03.2021, 23:31

общий

это ответ

Здравствуйте, gleb.babin!
Дано:
C=10^-6 Ф
f=10³ Гц
q_o=q_max=10^-5 Кл (*)
i₁=I_max
q₂=5*10^-6 Кл
Найти: L; t₁; t₂
Решение:
1. Период и частота колебаний связаны формулой
T=1/f (1)
Формула Томсона
T=2[$960$][$8730$](LC) (2)
Из (1) и (2)
[$8658$]
L=1/[(2[$960$]f)²*C] = 25 мГн
2. Уравнение колебаний заряда запишем через Cos, чтобы выполнялось условие (*)
q(t)=q_max*cos(2[$960$]f)t (3)
[$8658$]
q(t₂)=q_max*cos(2[$960$]f)t₂
5*10^-6=10^-5*cos(2[$960$]*10³)t₂
[$8658$]
cos(2[$960$]*10³)t₂=1/2
(2[$960$]*10³)t₂=[$960$]/3
[$8658$]
t₂=(1/6)*10^-3c
3. Уравнение колебаний силы тока в контуре найдем как производную заряда по времени:
i(t)=q'(t)
i(t)=-I_max*sin(2[$960$]f)t (4)
где I_max=(2[$960$]f)*q_max (5)
Тогда
i(t₁)=-I_max*sin(2[$960$]f)t₁
I_max=-I_max*sin(2[$960$]*10³)t₁
[$8658$]
sin(2[$960$]*10³)t₁=-1
(2[$960$]*10³)t₁=(3/2)*[$960$]
[$8658$]
t₁=(3/4)*10^-3c = 0,75 мс

Удачи

Об авторе:
С уважением
shvetski

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